scispace - formally typeset
Search or ask a question
Book

On fuzzy algorithms

01 Aug 1996-pp 127-147
TL;DR: A fuzzy algorithm is introduced which, though fuzzy rather than precise in nature, may eventually prove to be of use in a wide variety of problems relating to information processing, control, pattern recognition, system identification, artificial intelligence and, more generally, decision processes involving incomplete or uncertain data.
Abstract: Unlike most papers in Information and Control, our note contains no theorems and no proofs. Essentially, its purpose is to introduce a basic concept which, though fuzzy rather than precise in nature, may eventually prove to be of use in a wide variety of problems relating to information processing, control, pattern recognition, system identification, artificial intelligence and, more generally, decision processes involving incomplete or uncertain data. The concept in question will be called a fuzzy algorithm because it may be viewed as a generalization, through the process of fuzzification, of the conventional (nonfuzzy) conception of an algorithm. More specifically, unlike a nonfuzzy deterministic or nondeterministic algorithm (Floyd, 1967), a fuzzy algorithm may contain fuzzy statements, that is, statements containing names of fuzzy sets (Zadeh, 1965), by which we mean classes in which there may be grades of membership intermediate between full membership and nonmembership. To illustrate, fuzzy algorithms may contain fuzzy instructions such as:
Citations
More filters
Journal ArticleDOI
01 Jan 1973
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Abstract: The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.

8,547 citations


Cites background or methods from "On fuzzy algorithms"

  • ...A formal characterization of the concept of a fuzzy algorithm can be given in terms of the notion of a fuzzy Turing machine or a fuzzy Markoff algorithm [6], [7], [8]....

    [...]

  • ...Essentially, a fuzzy algorithm [6] is an ordered sequence of instructions ( Jike a computer program) in which some of the instructions may contain labels of fuzzy sets....

    [...]

  • ...what basis will such a number be chosen? As pointed out in [6], it is reasonable to assume that the result of execution will be that element of the fuzzy set which has the highest grade of membership in it....

    [...]

Book
31 Jul 1985
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

7,877 citations


Cites background from "On fuzzy algorithms"

  • ...The Determination of a Crisp Maximizing Decision Some authors [Kickert 1978; Nguyen 1979; Zadeh 1972] suggest approaches based on the notion of a maximizing set, which seem to have some disadvantages (see Wemers [19841)....

    [...]

Journal ArticleDOI
01 Jan 1997
TL;DR: This paper provides a tutorial on data fusion, introducing data fusion applications, process models, and identification of applicable techniques.
Abstract: Multisensor data fusion is an emerging technology applied to Department of Defense (DoD) areas such as automated target recognition, battlefield surveillance, and guidance and control of autonomous vehicles, and to non-DoD applications such as monitoring of complex machinery, medical diagnosis, and smart buildings. Techniques for multisensor data fusion are drawn from a wide range of areas including artificial intelligence, pattern recognition, statistical estimation and other areas. This paper provides a tutorial on data fusion, introducing data fusion applications, process models, and identification of applicable techniques. Comments are made on the state-of-the-art in data fusion.

2,356 citations

Journal ArticleDOI
TL;DR: A survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models.
Abstract: Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

1,575 citations

Journal ArticleDOI
TL;DR: F fuzzy logic is suggested, which is the logic underlying approximate or, equivalently, fuzzy reasoning, which leads to various basic syllogisms which may be used as rules of combination of evidence in expert systems.

1,278 citations

References
More filters
Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal ArticleDOI
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
Abstract: 1. Computing machines. 2. Definitions. Automatic machines. Computing machines. Circle and circle-free numbers. Computable sequences and numbers. 3. Examples of computing machines. 4. Abbreviated tables Further examples. 5. Enumeration of computable sequences. 6. The universal computing machine. 7. Detailed description of the universal machine. 8. Application of the diagonal process. Pagina 1 di 38 On computable numbers, with an application to the Entscheidungsproblem A. M. ...

7,642 citations

Journal ArticleDOI
TL;DR: This paper explores the foundations of, generalizes, and continues the work of Zadeh in [I] and [2].

2,375 citations


"On fuzzy algorithms" refers background in this paper

  • ...The grades of membership may be numbers in the interval [0, 1] or, more generally, points in a lattice (Goguen, 1967) or even a more general type of space....

    [...]

  • ...Fuzzy Algorithms L. A. ZADEH*...

    [...]

Book
01 Jan 1958

852 citations

Journal ArticleDOI
TL;DR: Algorithms to solve combinatorial search problems by using multiple-valued functions are illustrated with algorithms to find all solutions to the eight queens problem on the chessboard, and to finding all simple cycles in a network.
Abstract: Programs to solve combinatorial search problems may often be simply written by using multiple-valued functions. Such programs, although impossible to execute directly on conventional computers, may be converted in a mechanical way into conventional backtracking programs. The process is illustrated with algorithms to find all solutions to the eight queens problem on the chessboard, and to find all simple cycles in a network.

333 citations